Theorems · Definition · group theory

LinearOrderedCommGroup.Subgroup.genLTOne

{G : Type u_1} →
  [inst : CommGroup G] →
    [inst_1 : LinearOrder G] → [IsOrderedMonoid G] → (H : Subgroup G) → [Nontrivial ↥H] → [hH : IsCyclic ↥H] → G

Given a subgroup of a cyclic linearly ordered commutative group, this is a generator of the subgroup that is < 1.

Defined in

Mathlib.Algebra.Order.Group.Cyclic

Cited by

12 results in Mathlib

Foundations

Depth 79 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommGroupLinearOrderIsOrderedMonoidNontrivialIsCyclic